Elorza is a Basque surname. Notable people with the surname include:
Cosme Damián de Churruca y Elorza (1761–1805), Basque Spanish noble, admiral and politician Jorge Elorza (born 1976), American law professor and politician Julián Elorza Aizpuru (1879–1964), Spanish politician Pablo Elorza (born 1982), Argentine bass player, composer, arranger, author, producer and educator Patricia Elorza (born 1984), Spanish handball player